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Solving Word Problems based on a system Linear Equations

Last updated over 2 years ago
4 questions
I have given 2 problems and their solutions below.
You need to find a strategy (steps you can follow or some format you can use) to solve word problems using the answers given below.
1

Question:
The sum of two number is 14 and their difference is 2. Find the numbers.

Answer:
Let the two numbers be x and y.
x + y = 14 ………. (i)
x - y = 2 ………. (ii)
Adding equation (i) and (ii), we get 2x = 16 because +y -y = 0;
or, 2x/2 = 16/2 or, x = 16/2
or, x = 8 Substituting the value x in equation (i), we get
8 + y = 14
or, 8 – 8 + y = 14 - 8
or, y = 14 - 8
or, y = 6 Therefore, x = 8 and y = 6
Hence, the two numbers are 6 and 8.

What steps do you observe here that helped solve the problem. Summerize.

1

Question:

If twice the age of the son is added to the age of the father, the sum is 56. But if twice the age of the father is added to the age of the son, the sum is 82. Find the ages of father and son.  Answer: Let father’s age be x years
Son’s ages = y years
Then 2y + x = 56 …………… (i)
And 2x + y = 82 …………… (ii)  Multiplying equation (i) by 2, (2y + x = 56 …………… × 2)we get


or, 3y/3 = 30/3
or, y = 30/3
or, y = 10 (solution (ii) and (iii) by subtraction) Substituting the value of y in equation (i), we get;
2 × 10 + x = 56
or, 20 + x = 56
or, 20 – 20 + x = 56 – 20
or, x = 56 – 20
x = 36


Does your strategy from above work in this situation?
If not, what changes do you need to make?

1

Share your strategy with your partner and see if any further modification is necassary.

1

Using the above strategy, find solve the following question:

Two pens and one eraser cost Rs. 35 and 3 pens and four erasers cost Rs. 65. Find the cost of the pencil and the eraser separately.